a(n) = binomial(n, [n/2]) - 2.

Terms

a(0) =-1a(1) =-1a(2) =0a(3) =1a(4) =4a(5) =8a(6) =18a(7) =33a(8) =68a(9) =124a(10) =250a(11) =460a(12) =922a(13) =1714a(14) =3430a(15) =6433a(16) =12868a(17) =24308a(18) =48618a(19) =92376a(20) =184754a(21) =352714a(22) =705430a(23) =1352076a(24) =2704154a(25) =5200298a(26) =10400598a(27) =20058298a(28) =40116598a(29) =77558758